Nonlocal Description of the Nucleus-Nucleus Interaction

Abstract

A parameter-free nonlocal double-folding-inspired interaction is proposed for the nucleus-nucleus systems. Excellent reproductions of elastic scattering differential cross section data were obtained for several systems over a wide range of bombarding energies. Our results should be of value in the description of the scattering of other many-body systems. [S0031-9007(97)05269-1] PACS numbers: 21.30. Fe, 25.70.Bc The mean field interaction between complex quantum many-body systems (nucleus-nucleus, cluster-cluster, etc.) is still an open question in current physics research. The study of this matter is a fundamental step in the understanding of many-body dynamics. In the nucleus-nucleus case, significant progress has been achieved concerning this question during the last decade [1], as a consequence of the measurement of accurate and extensive elastic scattering data at intermediate energies. Nuclear rainbow scattering, first observed in a systems [2][3][4] and later in light heavy ions [5][6][7], probes the nucleus-nucleus potential not only at the surface region but also at smaller distances, and ambiguities in the real part of the potentials have been removed. The resulting phenomenological interactions have significant dependence upon the bombarding energies. Some theoretical models have been developed to account for this energy dependence through realistic mean field potentials. Nowadays, the most successful models seem to be those based on the DDM3Y interaction [8][9][10] which is an improvement of the originally energyindependent double-folding potential [11]. But, in order to fit the data, the density-and energy-dependent DDM3Y potential needs a renormalization factor which besides being system dependent [1,12] is still slightly energy dependent [1].In this Letter we show, by an extensive description of elastic scattering data using an optical integro-differential equation, that the dependence on the bombarding energy of the real bare potential is mostly due to the intrinsically nonlocal nature of the effective one-body interaction. The real bare potential (by bare we mean the average, mean field, interaction with no coupled channels effects) is constructed using the folding model. It contains no adjustable parameters and is energy independent. The absorptive part is taken to be a three parameters WoodsSaxon interaction. We also supply a simple approach to obtain the local-equivalent energy-dependent potential.Before we set the stage for the analysis of elastic scattering data, we first describe our theoretical model.When dealing with nonlocal interactions, one is required to solve the integro-differential equationwhere, on physical grounds [13], the kernel function is taken to be symmetric: U͑ R, R 0 ͒ U͑ R 0 , R͒. We take for U͑ R, R 0 ͒ the following form motivated by the physics problem at handIn our analysis, the Coulomb interaction, V C ͑R͒, was obtained using an expression for the double sharp cutoff folded potential [14] and the local energy-dependent imaginary potential, W ͑R, E͒, was taken t...

Non-local effects on the heavy-ion fusion at sub-barrier energies

“…Thus we assume a local energy-independent imaginary potential of the total optical potential and a corresponding local electromagnetic interaction. We can write [9,10] …”

“…In Refs. [8][9][10], the Jackson-Johnson idea was extended to heavier systems and the resulting potential, which is a modification of the doublefolding one, was shown to be quite accurate in accounting for a large body of elastic scattering data for a wide range of systems, including 16 O + 208 Pb. The PB non-locality was originally derived for neutron-nucleus scattering.…”

“…The São Paulo potential (SPP) has been in use for about one decade, especially in the analysis of heavy-ion elastic scattering data [9,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. It is based in part on the idea of single folding employed for alpha-nucleus scattering by Jackson and Johnson [27] in order to get the Perey-Buck (PB) nonlocal effects [28] extended to heavy ions.…”

“…For neutron-nucleus systems, Perey and Buck have associated the nonlocal interaction with a Woods-Saxon shape potential. For nucleus-nucleus, we have associated [9,10] the energy-independent nonlocal real potential V NL [(R + R )/2)], that appears in the PB and FL form, with the double folding potential,…”

“…Of course, when used in coupled-channel calculations, the non-locality is transformed into a non-dispersive energy dependence. In so far as the Pauli non-locality is concerned, the resulting locally equivalent nondispersive energy dependent potential has been constructed by our group [8][9][10][11] and it is coined the São Paulo potential. We shall use this potential here to investigate the relevance of the Pauli, exchange, non-locality on the fusion cross section at energies around the barrier.…”